This invention relates generally to techniques used to automatically determine correlations between corresponding recognizable signal elements. More particularly, the invention relates to automatic identification of sampled geophysical signal elements by type, determination of characterizing features of these elements and the use of these features in a search for corresponding elements within a system of related search bounds. The determination of displacements between elements found to be corresponding are useful in investigating subsurface formations.
The properties of subsurface formations of the earth vary considerably with depth. This variation may occur abruptly forming boundaries separating one earth formation from another. These boundaries vary in depth and inclination or dip from the earth's surface. When the direction or the degree of dip changes, structures are often formed which are potential hydrocarbon traps. Thus the recognition and mapping of formation boundaries is important to the oil and gas industry.
In seismic measurements acoustic waves are transmitted from the surface and reflected by such boundaries. The reflections or events, as they are known, are measured at the surface using horizontally spaced geophones. U.S. Pat. No. 3,681,748 entitled, "Velocity Stack Processing of Seismic Data" issued Aug. 1, 1972 to Emory E. Diltz illustrates a method of employing specific event information, limited through predetermined velocity-time patterns, to present event data in the velocity-time domain. Since time, in such cases, may be regarded as a function of formation depth, such presentations may reflect the inclination of formation boundaries with depth and horizontal displacement.
A more direct method of measuring the dip and the direction or azimuth of the dip of subsurface formations employs a dipmeter tool passed through a borehole drilled into the subsurface formations. These tools employ various means to obtain signals representative of variations of formation properties and, in particular, representative of formation boundaries intersecting the borehole. The signals are typically taken from at least three points radially spaced apart on the surface of the borehole. One such tool is described in the paper, THE HIGH RESOLUTION DIPMETER TOOL, by I. A. Allaud and J. Ringot published in the May-June, 1969 issue of "The Log Analyst".
In determining the inclination of a formation boundary from dipmeter signals, the signals obtained from one point on the borehole surface are correlated to determine displacements from corresponding signals obtained from at least two additional points. Two such displacements may determine the position of a plane representing the correlation portion of the signals. The method assumes that the correlated portion of the signal may represent some common feature of the formation.
The correlation of signals to determine displacements is typically accomplished by use of relatively standard correlation techniques. A paper describing one such technique and providing several correlation functions for such use is COMPUTER METHODS OF DIPLOG CORRELATION by L. G. Schoonover and O. R. Holt published in the February 1973 issue of "Society of Petroleum Engineers Journal". To determine displacements, cross correlation functions are applied to pairs of corresponding signals located within identical finite-length intervals called correlation intervals. A correlation function is used to determine the degree of likeness or correlation coefficient for the signals in these intervals.
The finite length correlation intervals used in dipmeter correlation usually comprise a large number of samples corresponding to about three feet of borehole recording. A series of coefficients are determined for a series of possible corresponding correlation intervals taken at different displacements between the intervals. These intervals are systematically selected within a search interval placed about some first assumed depth displacement. Normally the search interval is also of finite length. It is measured on one of the signals in directions both above and below the first assumed displacement. One signal may be considered as a base or reference signal and the other signal as a comparison or search signal. The search intervals are usually taken on the comparison signal.
For example, let S.sub.1 and S.sub.2 designate respectively the signals considered as the reference signal and the comparison signal. The correlation process considers a finite interval X of S.sub.1 and computes the correlation coefficient for a comparison interval X' of the same length on S.sub.2. The comparison interval is systematically moved from a first assumed displacement to successively displaced intervals on S.sub.2 within the search intervals. A coefficient C(d) to be defined below is computed for each such displacement.
Commonly signals are recorded digitally as discrete samples S(n) versus constant increments of time or depth. Thus the signals S.sub.1 (n) and S.sub.2 (n) are available as two series of discrete samples each series varying as the value of n. One correlation coefficient C(d) computed between given intervals X' and X' may be expressed as: ##EQU1## where:
d is the displacement between the correlation interval X and the comparison interval X'.
N is the number of samples in each interval, X or X'.
S.sub.1 (n) is the value of the (n)th sample of signal S.sub.1 in the correlation interval X.
S.sub.2 (d+n) is the value of the (n)th sample of signal S.sub.2 in a comparison interval X' displaced d samples from X. ##EQU2##
The displacement d which gives the coefficient C(d) corresponding to the best correlation is taken as the displacement between the samples 1 through N of S.sub.1 and samples (d+1) and (d+N) of S.sub.2.
Even though such expressions may use amplitude and mean value normalization features, they necessarily include the effects of using finite length and arbitrarily placed intervals of the signal. In addition, the length of the correlation interval often determines the type of signal features represented in the value of the best correlation function.
The ends of the finite correlation intervals are usually chosen in an automatic and arbitrary manner. Abnormal sample values occurring near the end portions of the intervals considered in the computation may cause the correlation coefficient to suffer from so called "end effects". These effects may lead to ambiguous values of the correlation coefficient. An improvement on the use of correlation techniques is described in copending application--"Well Logging Depth Correlation Technique", U.S. Ser. No. 70,709, filed Sept. 9, 1970 by David H. Tinch et al and now abandoned.
The finite interval method of correlation requires changing the correlation interval to include many samples of the corresponding signals in order to compare long duration signal features and few samples in order to compare short duration features. Further, when two features or signal elements present on the correlation interval on one signal separated by a first separation are compared with two corresponding features present on a second signal but here separated by a different separation, distorted correlation coefficients may result. Since an identical number of samples is required in each interval, it is difficult to compare two or more corresponding features present in the same correlation intervals but at different separations. One attempt at handling this problem is described in U.S. Pat. No. 3,700,815, "Automatic Speaker Verification by Non-Linear Time Alignment of Acoustic Parameters" issued Oct. 24, 1972 to Doddington et al. This patent describes a method of piece-wise resampling one of the two signals within intervals between signal features. The newly formed or warped samples are then reused in a correlation process. Unfortunately this process also distorts displacements between corresponding features within the warped interval.
Additional U.S. patents describing typical correlation processes and uses of displacements between best comparing signal intervals are U.S. Pat. No. 2,927,656 entitled, "Method and Apparatus for Interpreting Geophysical Data" issued Mar. 8, 1960 to F. J. Feagin, et al and U.S. Pat. No. 3,550,074 entitled, "Method for Determining the Static Shift Between Geophysical Signals" issued Dec. 22, 1970 to C. W. Kerns et al. Whether the simple amplitude difference or the more complex mean value formulas are used to compute the correlation coefficients, each such computation is still repeatedly performed on numerous samples within a preset correlation interval systematically displaced on one of the corresponding signals. The computation is performed usually without examining the type or duration of the signal features actually present. Thus many unproductive computations are performed on intervals which may not even contain significant signal features. Further, the computations may be performed on features of completely different characteristics which in addition to wasting valuable time, may give rise to erroneous miscorrelations.
It is an object of this invention to provide a new technique of determining correlations between features or elements of sampled signals representing variations of measured properties.
A further object is to determine at the same time reliable comparisons between elements of sampled signals represented by varying numbers of samples.
It is an object of this invention to provide an automatic technique of recognizing signal elements representing a variety of features.
It is a further object of the invention to provide a new and improved technique of comparing two or more sample intervals to determine the degree of correspondence of these intervals.
A further object is to provide a correlation technique wherein the intervals to be correlated are determined in a nonarbitrary method.
An additional object is to provide an efficient and accurate method of comparing two signal elements to determine their degree of correspondence.
In particular, an object of the invention is to provide a method of comparing signal intervals of unequal length.
A further object is to provide a technique for comparing signal elements wherein the possibility of making an error and wasting processing capacity in comparing elements which could not possibly correspond is reduced.
A further object of the invention is to provide a technique for properly considering the case where an element present on one signal has no corresponding element.
Further, it is an object to prevent the determination of a false correlation indication in cases where there is no comparable element or where there is only a doubtful comparison.
It is a further object to provide an improved technique of comparing correlations for more than one possible corresponding feature or element of a sampled signal.
It is a still further object to compare correlations corresponding to correlation coefficients or degree of comparison to determine the resolution of such comparisons and still further, the quality of the comparison itself.
An additional object is to provide a technique of correlation wherein only signal features or elements which are of comparable types are compared.
A still additional object is to provide a method of determining comparisons of signal elements of varying significance.
A particular object is to provide a method where the more significant elements are compared to determine reliable corresponding elements.
It is an object of the invention to produce a significant increase in the number of reliably determined correspondences between elements of sampled signals.
It is also an object to provide reliable correspondences between signal elements representing large features as well as small features of sampled signals without the necessity of recomputing with different correlation lengths or correlation functions for this purpose.
More particularly, it is an object to provide a technique to compare only those elements known to be within reasonable limits for displacements between such elements, and wherein such limits are automatically narrowed in a rational manner.
An additional object of the invention is to provide an efficient method of automatically reducing search intervals used in the search and comparison of possibly corresponding signal elements.
It is an object of the invention to provide a new method of determining displacements between corresponding portions of sampled signals.
It is an additional object to determine improved displacement value between corresponding signal elements.
It is a further object to determine corresponding signal elements and the displacements between such elements.
It is an object to provide a new method of correlating sampled signals to determine displacements between samples of these signals.
In accordance with the techniques of the present invention, a method for automatically determining with a machine and without human intervention correlations between characteristic signal elements corresponding to recognizable features as represented by discrete samples of the signals comprises processing the samples to recognize groups of samples representing specific types of elements selected to correspond to significant signal features. Characteristic parameters are determining according to the type of element and compared to determine which elements correspond to one another. In accordance with further features of the invention, characteristic parameters are compared for elements located within predetermined bounds of possible corresponding elements. These bounds may be determined by searching and sorting boundary positions according to pre-established laws of corresponding positions to provide provisional bounds for use in searching for possible corresponding elements. The parameters determined for elements located within provisional search bounds are compared and if an acceptable comparison is found, the corresponding bounds are modified to indicate subsequent search bounds for use in searching for additional possible corresponding elements.
In accordance with additional features of the invention, several specific types of elements of varying significance are recognized. Further, the specific types of elements are classified by using given ranges of thresholds for identifying various sizes of elements corresponding to a range of significance for elements of a given type. Still further, the parameters of elements of the more significant types are compared and if an acceptable comparison is found, the corresponding bounds are modified to indicate bounds for use in searching for possible corresponding elements of less significant types.
The steps of comparing parameters of elements of a given type located within previously provided search bounds and modifying bounds corresponding to elements found to correspond to provide further search bounds are repeated for remaining elements until all elements have been processed.
The displacements between elements and boundaries found to be corresponding may be taken as representing the displacement between corresponding signal features. If the signals are from a dipmeter tool, for example, the displacements may be used to determine the attitude of a geological feature relative to the position of the tool and when provided with the tool position, they may be used to determine the strike and dip of the geological features.
Also, the displacements may be used to align displaced signals by applying alignment corrections. The signals then aligned on common geological features may be properly combined and used for further evaluation of subsurface formations.
For a better understanding of the present invention, together with other and further objects thereof, reference is had to the following description taken in connection with the accompanying drawings, the scope of the invention being pointed out in the appended claims.